case 10 failed: tile 511 overlaps input: 0100110011001101001101110111101100011110010000110111001001011001001000000110110000011111010011001011101111000111000000001010100111111111010111111100011111010100111010101111010110001110101110000010000111001110111100011101110000001000111100111000010100101000101001111101001101011010000110111100001111101110011001101001100111010111000010000110011111010001011011011110000001110011111110100101110001111011011011000001111001010111100111101111010000011111100101101100001010101101111000010010000101101011010100111100011110110001101000100100100 output: 1 1 1 3 3 1 1 1 3 1 3 3 3 1 1 1 3 1 3 3 3 1 1 1 3 1 3 3 3 1 1 1 1 1 3 1 1 1 1 3 1 1 1 3 3 1 3 3 3 1 1 1 1 1 1 3 1 1 3 1 1 3 1 1 1 3 3 3 1 3 2 1 3 1 3 3 3 1 1 1 3 3 1 3 1 3 3 3 1 3 3 3 2 3 3 3 1 1 1 3 3 1 3 3 3 1 1 1 3 1 3 3 1 2 2 3 1 1 4 1 1 1 3 1 1 3 1 3 1 1 1 1 1 3 3 1 1 1 3 1 1 1 3 1 1 1 3 3 2 2 3 1 1 1 1 1 3 1 3 3 1 4 3 4 1 4 4 1 4 3 4 1 4 3 4 1 3 4 1 3 1 1 1 1 1 3 4 3 3 1 1 1 1 2 3 1 1 1 3 1 1 1 1 3 3 3 4 2 1 3 3 2 1 1 3 1 1 1 1 3 3 1 3 3 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 3 3 2 2 1 3 3 3 3 1 1 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 3 1 2 1 3 1 1 4 1 3 1 2 1 1 1 4 1 3 1 1 1 3 3 1 3 3 3 3 1 3 3 3 1 3 3 3 1 3 1 1 1 3 3 3 1 1 1 3 1 3 3 3 1 3 3 1 3 1 3 3 3 3 1 1 1 3 1 2 1 1 1 3 3 1 3 1 3 1 1 4 1 1 1 3 1 1 1 3 1 3 3 3 1 3 3 1 3 1 3 3 3 1 1 3 1 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1 3 3 3 3 3 1 1 1 3 3 1 1 3 1 1 3 1 2 1 3 3 1 1 1 3 1 1 1 3 1 3 3 3 1 3 1 1 4 1 3 1 1 1 3 3 3 1 3 3 3 1 1 1 3 1 1 1 3 1 1 1 3 1 3 3 1 3 3 3 1 3 3 3 1 1 1 3 3 1 1 3 1 1 3 1 2 1 3 3 1 3 3 3 1 3 1 1 3 3 1 3 1 3 3 3 1 1 1 3 4 1 1 1 3 1 1 1 3 1 3 3 1 3 1 3 3 3 3 3 1 1 1 3 1 1 1 3 3 1 1 1 1 1 3 1 1 3 3 1 1 1 3 3 3 1 1 1 1 3 1 1 1 1 3 1 1 1 3 1 1 1 1 3 1 1 3 1 1 3 3 1 2 1 1 1 1 3 3 3 1 3 3 3 1 1 1 3 1 1 1 3 1 1 1 3 4 1 3 1 2 1 3 3 1 3 1 1 4 1 1 1 3 1 3 1 2 1 3 3 1 1 1 3 3 3 1 3 1 1 1 3 3 3 1 3 1 1 1 3 1 3 1 1 3 3 1 3 1 1 1 3 1 3 3 3 1 3 3 3 1 1 1 3 3 3 1 3 3 3 1 3 1 1 1 3 3 3 1 3 1 1 1 3 1 1 1 3 1 3 1 1 3 3 1 3 3 3 1 3 1 3 1 1 4 1 1 1 3 1 3 3 3 1 3 1 2 1 1 1 4 1 1 1 3 1 1 1 3 1 1 1 3 1 3 1 2 1 1 1 3 3 1 3 4 1 3 1 2 1 1 1 4 1 3 1 2 1 3 3 1 1 1 3 3 3 1 3 1 3 1 1 4 1 3 1 1 1 3 3 1 3 3 3 3 1 3 3 3 1 3 3 1 3 3 3 3 1 1 1 1 3 1 1 1 1 1 3 3 1 1 3 3 3 1 3 3 3 1 1 1 3 1 1 1 3 1 3 3 3 1 1 1 3 4 1 1 1 3 1 3 3 3 1 3 3 3 1 1 1 3 1 3 3 3 1 3 3 3 1 3 1 2 1 1 1 4 1 1 1 3 1 3 3 1 3 3 3 1 3 3 3 1 3 3 3 1 1 1 3 1 1 1 3 3 1 1 3 1 1 1 1 3 1 3 3 3 1 3 1 2 1 3 3 1 3 3 3 1 3 1 1 3 3 1 3 1 3 1 1 3 3 1 3 1 1 1 3 4 1 3 1 2 1 1 1 3 3 1 3 3 3 1 3 4 1 1 1 3 1 3 1 1 1 3 3 1 3 3 3 1 3 1 3 3 3 1 1 3 1 3 1 1 1 3 3 3 1 3 3 1 3 1 3 3 3 3 1 3 3 1 1 1 3 3 1 2 1 3 3 1 2 2 4 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1